In this section we establish the asymptotic behaviour of the generalised posterior under the [1]} loss \(\ell (\theta ; \mathbf {y}) = \ell _{TW}(\theta ; \mathbf {y})\)  given by (REF ). Initially, in Section REF , we consider the case, as assumed by [1]}, that the design points \(\mathbf {x}_1, \dots , \mathbf {x}_n\)  are an independent and identically distributed sample from a uniform distribution on \(\mathcal {X}\) . Then, in Section REF , we consider the behaviour conditional on \(\mathbf {d} = \left\lbrace  \mathbf {x}_1, \dots , \mathbf {x}_n \right\rbrace \) .
